q-Fractional Hesitant Fuzzy Sets and Their Correlation Coefficients: Multi-Criteria Decision Making Technique for Selection of Agricultural Land to Cultivate Apples Crops

The q-Fractional Fuzzy Sets (q-FrFSs) offers information in Membership Grade (MG) and Non-membership Grade (NMG) of an object; however, both grades have the hesitancy factor because complex information usually does not give single MG and single NMG. Therefore, in this study we initiate the concept of q-Fractional Hesitant Fuzzy Sets (q-FrHFSs) and its basic properties. In q-FrHFSs not only hesitancy factor is taken into account but it also consider all possible values of uncertainties in [0, 1]×[0, 1]. Thus Correlation Coefficients (CCs) on q-FrHFSs are necessary to cope uncertain information with hesitancy, MGs and NMGs. In this study we introduce two types of CCs namely CCs on q-FrHFSs and weighted CCs on q-FrHFSs. We investigate underlying properties of these CCs and give a MCDM method on q-FrHFSs environment. We consider an application of our method to agricultural land selection across a set of cities for cultivation of apples crop. At the end, we compare our method of q-FrHFSs to some existing frameworks.